Question

type in the five - number summary for the data shown on the right. the minimum of the data is. the first quartile is. the median of the data is. the third quartile is. the maximum of the data is. movie length (minutes) 8 1 3 9 0 3 7 10 4 4 7 9 11 1 3 5 12 5 9 9 13 2 6 done

Explanation:

Step1: Write out data set

The data set from the stem - and - leaf plot is: 81, 83, 90, 93, 97, 104, 104, 107, 109, 111, 113, 115, 125, 129, 129, 132, 136.

Step2: Find minimum

The minimum value is the smallest number in the data set. So, the minimum is 81.

Step3: Find first quartile ($Q_1$)

First, find the median of the lower half of the data. There are 17 data points. The lower half consists of the first 8 data points. The median of 81, 83, 90, 93, 97, 104, 104, 107 is $\frac{93 + 97}{2}=95$.

Step4: Find median ($Q_2$)

Since there are 17 data points, the median is the 9th - ordered value. The median is 109.

Step5: Find third quartile ($Q_3$)

Find the median of the upper half of the data. The upper half consists of the last 8 data points. The median of 111, 113, 115, 125, 129, 129, 132, 136 is $\frac{125+129}{2}=127$.

Step6: Find maximum

The maximum value is the largest number in the data set. So, the maximum is 136.

Answer:

The minimum of the data is 81.
The first quartile is 95.
The median of the data is 109.
The third quartile is 127.
The maximum of the data is 136.